More particles as more area is painted
As I haven't found any solution so far and this fixed-count workflow limits my daily work a lot, I have refreshed my "so-so programming skills" and I ended up with creating a Blender (2.79) addon which does this job for me.

With the addon, you set the Density parameter and the Emmission Number is adjusted accordingly:



I have placed the addon to Github and would be very happy is someone can test it and report any bugs.
https://github.com/jendabek/blender-particles-density